my office computer is hooked up to the office network (internet is available).
my laptop is wifi connected to a public guest network (internet is available).
how can I connect these two pc(s) with multiplicity?
You are going to need to get them both on a shared subnet. The best \ easiest way to do that is via a VPN connection.
Once they both on that same subnet, you can connect to each their respective VPN issued IP addresses.
Stardock Product Lifecycle Manager